The Extended Flexible Dirichlet model: a simulation study

Compositional data are prevalent in many elds (e.g. environmetrics, economics, biology, etc.). They are composed by positive vectors subject to a unitsum constraint (i.e. they are dened on the simplex ), proportions being an example of this kind of data. A very common distribution on the simplex is the Dirichlet, but its poor parametrization and its inability to model many dependence concepts make it unsatisfactory for modeling compositional data. A feasible alternative to the Dirichlet distribution is the Flexible Dirichlet (FD), introduced by Ongaro and Migliorati [1]. The FD is a generalization of the Dirichlet that enables considerable exibility in modeling dependence as well as various independence concepts, though retaining many good mathematical properties of the Dirichlet. More recently, the Extended Flexible Dirichlet (EFD, [2]) distribution has been proposed in order to generalize the FD. The EFD preserves a nite mixture structure as the FD, but it exhibits some relevant advantages over the FD, such as a more exible cluster structure and a (even strong) positive dependence for some pairs of variables. The aim of this contribution is twofold. First we propose and investigate sophisticated EM algorithms for parameters estimation, with particular emphasis on the initialization problem, which is a crucial issue. Furthermore, we devise a simulation study to evaluate the performances of the MLE of the parameters as well as of a procedure proposed to compute their standard errors.